Mulltiple steady states in microvascular networks

Abstract

The computation of steady state blood flow requires the simultaneous solution of three conservation laws at each junction point in the network. First the RBC mass balance must be satisfied. This is governed by nonlinear equations at diverging junctions – the plasma skimming rule. The second conservation law is the momentum balance (or pressure distribution). Again this momentum balance is governed by a nonlinear function – the Fahraeus‐Lindqvist effect for apparent viscosity. Finally, the total mass balance for volumetric blood flow is a linear system of equations that must be satisfied. This nonlinear system can result in multiple steady states as network parameters are varied. Many of these multiple steady states arise from what are called saddle node bifurcations in the nonlinear dynamics.The same network can have steady states with different flow, hematocrit and pressure distributions. Some may be attractive, while others are repulsive. The system can exhibit hysteresis. These results can have significant physiological consequences on flow and hematocrit distributions in response to blood flow control action.Funding provided by UNH and Cornell University